U.S. patent number 5,545,192 [Application Number 08/348,257] was granted by the patent office on 1996-08-13 for intermittent use of bright light to modify the circadian phase.
This patent grant is currently assigned to Brigham and Women's Hospital. Invention is credited to Charles A. Czeisler, Richard E. Kronauer.
United States Patent |
5,545,192 |
Czeisler , et al. |
August 13, 1996 |
**Please see images for:
( Certificate of Correction ) ** |
Intermittent use of bright light to modify the circadian phase
Abstract
The present invention is a method for modifying the circadian
cycle of a human subject to a desired state including the steps of
determining the characteristics of the desired circadian cycle,
selecting an appropriate time during which to apply a light
stimulus to effect a desired modification of the present circadian
cycle, and applying the stimulus at the selected time to achieve
the desired circadian cycle for the subject. The light stimulus of
the present invention includes an episode of intermittent light
consisting of at least two pulses of enhanced light separated by at
least one pulse of reduced light.
Inventors: |
Czeisler; Charles A.
(Cambridge, MA), Kronauer; Richard E. (Cambridge, MA) |
Assignee: |
Brigham and Women's Hospital
(Boston, MA)
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Family
ID: |
23367250 |
Appl.
No.: |
08/348,257 |
Filed: |
November 28, 1994 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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218886 |
Mar 28, 1994 |
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97618 |
Jul 27, 1993 |
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882172 |
May 8, 1992 |
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819403 |
Jan 10, 1992 |
5304212 |
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521041 |
May 9, 1990 |
5167228 |
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365949 |
Jun 15, 1989 |
5176133 |
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66677 |
Jun 26, 1987 |
5163426 |
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521041 |
May 9, 1990 |
5167228 |
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365949 |
Jun 15, 1989 |
5176133 |
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66677 |
Jun 26, 1987 |
5163426 |
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Current U.S.
Class: |
607/88 |
Current CPC
Class: |
A61M
21/00 (20130101); A61N 5/0618 (20130101); A61M
2021/0044 (20130101); A61N 2005/0648 (20130101) |
Current International
Class: |
A61M
21/00 (20060101); A61N 5/06 (20060101); A61N
005/06 () |
Field of
Search: |
;607/88 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Other References
Bio-Brite, Inc. Light Visor.TM. Product Brochure. .
Bio-Brite, Inc. Light Visor.TM. Instruction Manual, 1992. .
"Healthy Food, Exercise Can Help Beat Jet Lag," USA Today Jan. 26,
1993. .
Light Glasses.TM. Brochure by Moodlighters, Inc. .
Casano, P., Light Glasses User's Guide Plus Using Bright Light to
Treat Jet Lag, First Edition (1992). .
Circadian Technologies, Inc., 1991 Products and Services Catalog.
.
Reinberg et al., "Circadian Rhythm Amplitude and Individual Ability
to Adjust to Adjust to Shift-Work," Ergonomics, vol. 21, No. 10
(1978) pp. 763-766. .
Czeisler et al., "Rotating Shift Work Schedules That Disrupt Sleep
Are Improved by Applying Circadian Principals," Science, vol. 217,
No. 4558 (1982) pp. 460-463. .
Czeisler et al., "Chronotherapy: Resetting the Circadian Clocks of
Patients With Delayed Sleep Phase Insomnia," Sleep, vol. 4, No. 1
(1981) pp. 1-21. .
Goodwin and Lewy, "The Use of Bright Light in the Treatment of
Chronobiologic Sleep and Mood Disorders: The Phase-Response Curve,"
Psychopharmacology Bulletin, vol. 19, No. 3 (1983) pp. 523-525.
.
Strogartz, The Mathematical Structure of the Human-Wake Cycle,
Lecture Notes in Biomathematics, No. 69, Springer-Verlag (1986)
239. .
Lewy et al., "Immediate and Delayed Effects of Bright Light on
Human Melatonin Production: Shifting Dawn and Dusk Shifts Dim Light
Melatonin Onset," Annuals, New York Academy of Sciences (1985) pp.
253-259. .
Lewy et al., "Antidepressant and Circadian Phase-Shifting Effects
of Light," Science, vol. 235, pp. 352-354. .
Honma et al., "Phase-Dependent Responses of Human Circadian Rhythms
to a Bright Light Pulse: Experiments in a Temporal Isolation Unit,"
J. Physiol. Soc., Japan (1986) p. 416. .
Czeisler et al., "Sleep Deprivation In Constant Light Phase Advance
Shifts and Shortens the Free-Running Period of the Human Circadian
Timing System," Sleep Research, vol. 14, p. 252. .
Brown et al., "A Method for Quantifying Phase Position of the Deep
Circadian Oscillator and Determining a Confidence Interval," Sleep
Research, vol 14 (1985) p. 290. .
Czeilsler et al., "Entrainment of Human Circadian Rhythms by
Light-Dark Cycles: A Reassessment," Photochemistry and
Photobiology, vol. 34 (1981) pp. 239-247. .
Daan et al., "A Functional Analysis of Circadian Pacemakers in
Nocturnal Rodents, II. The Variability of Phase Response Curves,"
Journal of Comparative Physiology, vol. 106 (1976) pp. 253-266.
.
Winfree, The Geometry of Biological Time, Springer-Verlag (1980)
pp. 36-38, 53. .
Saunders, "Circadian Rhythms: Entrainment by Light and Temperature"
(Chapter 3), An Introduction To Biological Rhythms Blackie (1977)
pp. 40-64. .
Hoban et al., "Light Effects on Circadian Timing System of A
Diurnal Primate, the Squirrel Monkey," American Journal of
Physiology, vol. 249 (1985) pp. R274-R280. .
Daan et al., "Scheduled Exposure to Daylight: A Potential Strategy
To Reduce Jet Lag Following Transmeridian Flight,"
Psychopharmacology Bulletin, vol. 20, No. 3 (1984) pp. 566-568.
.
Wever, The Circadian System of Man: Results of Experiments Under
Temporal Isolation, Springer-Verlag (1979) 276. .
Czeisler et al., "Circadian Rhythms and Performance Decrements in
the Transportation Industry," Proceedings of a Workshop on the
Effects of Automation on Operator Performance, Coblenz, A. M. ed.,
Commission Des Communautes Europeenes, Programme De Recherche
Medicale et de Sante Publique, Universite Rene Descartes: Paris
(1986) pp. 146-171. .
Kronauer et al., "Mathematical Model of the Human Circadian System
With Two Interacting Oscillators," American Journal of Physiology,
vol. 242 (1982) pp. R3-R17. .
Stevens, "To Honor Fechner and Repeal His Law," Science, vol. 133
(1961) pp. 80-86. .
Czeisler et al., "A Clinical Method to Assess the Endogenous
Circadian Phase (ECP) of the Deep Circadian Oscillator in Man,"
Sleep Research, vol. 14 (1985) p. 295. .
Wever et al., "Bright Light Affects Human Circadian Rhythms,"
European Journal of Physiology, Pfluegers Archiv. vol. 396 (1983)
pp. 85-87. .
Wever, "Use of Light to Treat Jet Lag: Differential Effects of
Normal and Bright Artificial Light on Human Circadian Rhythms,"
Annals New York Academy of Sciences, Part III, Health Effects of
Interior Lighting, (1985) pp. 282-304. .
Lingjaerde et al., "Insomnia During the `Dark Period` In Norther
Norway," Acta Psychiatr. Scand., vol. 71 (1985) pp. 506-12. .
Lewy et al., "Treatment of Appropriately Phase Typed Sleep
Disorders Using Properly Timed Bright Light," Sleep Research (1985)
p. 304. .
Kronauer et al., "A 2-Oscillator Model Derived from Free-running
Circadian Rhythms Accurately Predicts Range of Zietgeber
Entrainment," Sleep Research, vol. 12 (1983) p. 368. .
Czeisler et al., "Entrainment of Human Circadian Rhythms by
Light-Dark Cycles: A Reassessment," American Society for
Photobiology, Printed by University of Vermont (1978) p. 73. .
Aschoff et al., "Human Circadian Rhythms: A Multioscillatory
System," Federation Proceedings, vol. 35 (1976) pp. 2326-2332.
.
Eastman, "Bright Light Improves the Entrainment of Circadian Rhythm
of Body Temperature to a 26-Hour Sleep-Wake Cycle in Humans," Sleep
Research (1986) p. 271. .
Ehret et al., Overcoming Jet Lag, Berkley Books (New York) (1983)
160. .
Arendt et al., "Phase Response of Human Melatonin Rhythms to Bright
Light in Antarctica," Journal of Physiology, vol. 377 (1986) p. 68.
.
Kripke et al., "Bright White Light Alleviates Depression,"
Psychiatry Research, vol. 10 (1983) pp. 105-112. .
Czeisler et al., "Bright Light Resets the Human Circadian Pacemaker
Independent of the Timing of the Sleep-Wake Cycle," Science, vol.
233 (1986) pp. 667-671. .
Sinclair, and Response by Czeisler et al., "Moonlight and Circadian
Rhythms," Science, vol. 235 (1987) p. 145. .
PCT International Search Report, International Application No.
PCT/US88/02177, Search completed on Nov. 3, 1988. .
Czeisler et al., "Human Sleep: Its Duration and Organization Depend
on Its Circadian Phase," Science, vol. 210 (1980) pp. 1264-1267.
.
Miller, J., "Bright Lights Can Reset the Human Clock," New
Scientist (Jul. 15, 1989) p. 35. .
Long, M. E., "What is this thing called Sleep?," National
Geographic (Dec. 1987) pp. 786-832. .
Lewy et al., "Light Suppresses Melatonin Secretion in Humans,"
Sciences, vol. 210 (1980) pp. 1267-1269. .
"Scientists Find Shift Work May Be Hazardous to Heart," The
Washington Post, Section A8, (Jan. 5, 1992). .
"The Latest From the Jet Lag Front," Travel & Leisure, Aug.
1994. .
Nelson et al., "Sensitivity and Integration in a Visual Pathway for
Circadian Entrainment in the Hamster (Mesocricetus Auratus),"
Journal of Physiology 439:115-145 (1991). .
Kronauer et al., "Commentary: The Human Circadian Response to
Light-Strong and Weak Resetting," Journal of Biological Rhythms 8
(4) :351-360 (1993)..
|
Primary Examiner: Smith; Ruth S.
Attorney, Agent or Firm: Sterne, Kessler, Goldstein &
Fox P.L.L.C.
Government Interests
STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSORED
RESEARCH AND DEVELOPMENT
This invention was made with government support under Grant Nos.
1RO1AG04912-03 and 1RO1HD20174-01 awarded by the National Institute
of Health. The government has certain rights in the invention.
Parent Case Text
RELATED U.S. APPLICATIONS
This application is a continuation-in-part of Ser. No. 218,886,
filed Mar. 28, 1994 now abandoned, which is a continuation of Ser.
No. 97,618, filed Jul. 27, 1993 now abandoned, which is a
continuation of Ser. No. 882,172, filed May 8, 1992 now abandoned,
which is a continuation-in-part of Ser. No. 819,403, filed Jan. 10,
1992, now U.S. Pat. No. 5,304,212, which is a continuation of Ser.
No. 521,041, filed May 9, 1990, now U.S. Pat. No. 5,167,228 and
Ser. No. 365,949, filed Jun. 15, 1989, now U.S. Pat. No. 5,176,133,
both continuations-in-part of Ser. No. 66,677, filed Jun. 26, 1987,
now U.S. Pat. No. 5,163,426.
Claims
We claim:
1. A method of modifying a human subject's endogenous circadian
cycle to a desired state, comprising the steps of:
determining the characteristics of a desired endogenous circadian
cycle for said subject;
selecting an appropriate time with respect to the presumed phase of
physiological markers of the subject's present endogenous circadian
cycle during which to apply a light stimulus to effect a desired
modification of said present endogenous circadian cycle of said
subject, wherein said stimulus comprises an episode of intermittent
light consisting of at least two pulses of light of enhanced
intensity separated by at least one pulse of light of reduced
intensity and
applying said stimulus at said selected appropriate time to achieve
said desired endogenous circadian cycle for said subject.
2. The method of claim 1, wherein at least one of said pulses of
light of enhanced intensity has an intensity greater than
approximately 4,000 lux.
3. The method of claim 1, wherein at least one of said pulses of
light of enhanced intensity has an intensity between approximately
500-1,000 lux.
4. The method of claim 1, wherein at least one of said pulses of
light of enhanced intensity has an intensity between approximately
1,000-2,000 lux.
5. The method of claim 1, wherein at least one of said pulses of
light of enhanced intensity has an intensity between approximately
2,000-4,000 lux.
6. The method of claim 1, wherein at least one of said pulses of
light of enhanced intensity has an intensity between approximately
4,000-100,000 lux.
7. The method of claim 1, wherein at least one of said pulses of
light of reduced intensity has an intensity between approximately
0-200 lux.
8. The method of claim 7, wherein at least one of said pulses of
light of reduced intensity has an intensity between approximately
0-10 lux.
9. The method of claim 7, wherein at least one of said pulses of
light of reduced intensity has an intensity between approximately
10-50 lux.
10. The method of claim 7, wherein at least one of said pulses of
light of reduced intensity has an intensity between approximately
50-200 lux.
11. The method of claim 1, wherein approximately 20% of the
duration of said episode of intermittent light comprises light of
enhanced intensity.
12. The method of claim 11, wherein said episode of intermittent
light comprises an approximately 5 hour episode of approximately 25
minute cycles, each 25 minute cycle including approximately a 1
minute transition up to light of enhanced intensity, four minutes
of enhanced light, a 1 minute transition down to light of reduced
intensity, and 19 minutes of light of reduced intensity.
13. The method of claim 1, wherein greater than approximately 20%
of the duration of said episode of intermittent light comprises
light of enhanced intensity.
Description
FIELD OF THE INVENTION
The present invention relates to a new and improved method for
modifying the circadian cycle of a human subject. More
specifically, the present invention relates to a method for
modifying the circadian cycle by application of intermittent pulses
of bright light.
BACKGROUND OF THE INVENTION
It is known that humans exhibit circadian cycles in a variety of
physiologic, cognitive, and behavioral functions. The cycles are
driven by an internal biological clock or circadian pacemaker which
is located in the brain. It is also known that humans exhibit
different degrees of alertness or productivity during different
phases of their circadian cycle.
Often, the activities in which humans wish to engage do not
coincide with the most appropriate point in their circadian cycle.
For instance, transmeridian travelers experience what is commonly
referred to as "jet lag", due to the fact that their circadian
cycle is not "in tune" with the geophysical time of their
destination. In essence, the traveler's physiological cycle either
lags or leads their desired activity-rest schedule.
In a similar fashion, people who work in professions requiring them
to work at night, such as factory workers, medical personnel, and
police experience a desynchrony between the activities in which
they desire to engage and their physiological ability to engage in
such activities. Commonly known as "shift workers" these
individuals often experience an inability to sleep soundly during
their non-working hours.
Other sleep-related disorders thought to be related to the
misalignment of the circadian cycle with the desired activity-rest
schedule include delayed-sleep-phase insomnia,
advanced-sleep-phased insomnia and Seasonal Affective Disorder
(SAD).
It has been known for quite some time that the circadian cycle of
all animals (including humans) is sensitive to exposure to bright
light. Thus, it is recognized that the circadian cycle of an animal
may be adjusted or modified by exposing the subject to scheduled
"pulses" of bright light.
Although all animals are responsive to applications of bright
light, the responsiveness of the circadian pacemaker of all animals
is not the same. For example, the responsiveness of the circadian
pacemaker of a rodent is quite different than the responsiveness of
the circadian pacemaker of a human. Indeed, for over twenty years
it has been recognized that the response of the circadian pacemaker
to light in nocturnal rodents is principally developed during the
early time of light exposure (e.g., within the first 15 minutes
from the dark-adapted state) while subsequent protracted exposure
(e.g., 1-2 hours) generates relatively little additional phase
shift. Recently, these findings were considerably sharpened for the
case of the golden hamster. See Nelson, D. E. et al., "Sensitivity
and Integration in a Visual Pathway for Circadian Entrainment in
the Hamster (Mesocricetus Auratus),"Journal of Physiology, No. 439
(1991), pp. 115-145. A tradeoff between light intensity and
stimulus duration was demonstrated (i.e., brighter light requires
less duration), and at a modest level of light (e.g., 20 lux)
pseudo-saturation of the phase shift response was achieved in about
five minutes.
Superficially, the responsiveness of the human circadian pacemaker
to light is very different. Unquestionably, humans are less
sensitive, requiring several thousand lux of light and stimulus
durations of several hours to match rodent phase shifts achieved at
20 lux of light in 5 minutes. This is consistent, however, with the
high sensitivity of nocturnal rodents for all visual tasks. It was
recently discovered that a significant functional distinction
between rodents and humans is the fact that humans appear to sum
circadian photic responses progressively. For example, three hours
of exposure to bright light produces about 3/5 the phase shift of
five hours of exposure to light centered at the same point of the
circadian phase.
The apparently disparate functional characteristics of human and
rodent responses can actually be described as a manifestation of a
single model structure which is the subject of the present
invention.
SUMMARY OF THE INVENTION
In accordance with the objectives described above, the present
invention is a method of modifying the endogenous circadian cycle
of a human subject to a desired state comprising the steps of
determining the characteristics of a desired endogenous circadian
cycle, selecting an appropriate time with respect to the presumed
phase of physiological markers of the subject's present endogenens
circadian cycle during which to apply a stimulus to effect a
desired modification of the present endogenous circadian cycle, and
applying the stimulus at the selected appropriate time to achieve
the desired endogenous circadian cycle for the subject. The
stimulus comprises an episode of intermittent light consisting of
at least two pulses of light of enhanced intensity separated by at
least one pulse of reduced intensity.
At least one of the pulses of light of enhanced intensity may be
greater than approximately 4,000 lux. At least one of the pulses of
light of enhanced intensity may be between 500-1,000 lux. At least
one of the pulses of light of enhanced intensity may be between
1,000-2,000 lux. At least one of the pulses of light of enhanced
intensity may be between 2,000-4,000 lux. At least one of the
pulses of light of enhanced intensity may be between 4,000-100,000
lux.
At least one of the pulses of light of reduced intensity may be
between 0-200 lux. At least one of the pulses of light of reduced
intensity may be between 0-10 lux. At least one of the pulses of
light of reduced intensity may be between 10-50 lux. At least one
of the pulses of light of reduced intensity may be between 50-200
lux.
The episode of intermittent light may comprise a 5-hour episode of
approximately 25-minute cycles, each 25-minute cycle including a
1-minute transition up to light of enhanced intensity, four minutes
of enhanced light, a 1-minute transition down to light of reduced
intensity and 19-minutes of light of reduced intensity.
Approximately 20% of the duration of the episode of intermittent
light may be light of enhanced intensity.
In another aspect, the present invention is an apparatus for
applying a light stimulus to a human subject to achieve a desired
endogenous circadian cycle comprising an enhancing means for
exposing the subject to light of enhanced intensity, a reducing
means for exposing said subject to light of reduced intensity and a
controlling means for controlling exposure of the subject to light
of enhanced intensity and light of reduced intensity. The apparatus
may also include a photosensor. The apparatus may be incorporated
into a pair of eyeglasses or a visor.
BRIEF DESCRIPTION OF THE DRAWINGS
The method of the present invention is best understood and
appreciated by referring to the accompanying drawings in which:
FIG. 1 is a graphic representation of what was thought to be the
response of the circadian pacemaker to pulses of enhanced and
diminished light;
FIG. 2 is a graphic representation of a second theory as to how the
circadian pacemaker responded to pulses of enhanced and diminished
light; and
FIG. 3 is a graphic representation of the response of the circadian
pacemaker to pulses of enhanced and diminished light based on the
photic transducer model of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
Several methods for assessing and modifying the circadian cycle of
a human subject are disclosed and claimed in the patents and
applications listed in the RELATED U.S. APPLICATIONS section of
this document. The disclosures of the listed patents are
incorporated, in their entirety, into the present application by
reference. While the circadian cycle of a human subject may be
successfully assessed and modified by the methods disclosed in each
of these patents, subsequent research has shown that the circadian
cycle may be modified more efficiently by a model based on a photic
transducer which reflects the recent finding that humans appear to
sum circadian photic responses progressively.
Although not fully addressed in the present disclosure, it must be
remembered that prior to modifying the circadian phase of a human
subject to a desired state, the present circadian cycle of the
subject must first be assessed. The subject's present circadian
cycle may be successfully assessed using any of the techniques
disclosed in the patents previously listed in this document and
such assessing techniques are specifically incorporated into the
present disclosure by reference.
Prior to discussing the improved model of the present invention, it
may be helpful to briefly discuss the development of circadian
models over the past several years. It was originally thought that
in order to rapidly shift the circadian phase the subject must be
exposed to a bright light stimulus of high intensity (e.g., 10,000
lux) for a long period of time (e.g., 5 hours). As shown in FIG. 1,
it was believed that the circadian pacemaker was immediately
responsive to exposure to light and that such a level of
responsiveness was maintained until exposure to the light stimulus
was interrupted. As the light stimulus was interrupted, it was
thought that no further response of the circadian pacemaker could
be evoked and that the circadian pacemaker was instantaneous in
nature, as its responsiveness to a light stimulus was initiated and
terminated precisely with the timing (or onset and offset) of the
light stimulus.
Subsequent research indicated, however, that the circadian
pacemaker did not respond to light stimuli as previously thought.
With reference now to FIG. 2, a second theory was developed which
was based on the premise that an increase in retinal light exposure
requires a measurable duration of time (time ramp A) to initiate
the neurophysiologic or neurohumoral chain of events responsible
for mediating the circadian response to enhanced light exposure and
that these biological effects of enhanced light on the circadian
pacemaker will persist on a diminishing trajectory (time ramp B)
for some duration of time following a reduction in the level of
retinal light exposure. Thus it was thought that the circadian
pacemaker continued to respond on a diminishing scale to the
previous light stimulus even though the subject was being exposed
to an episode of darkness (or an interruption of the light stimulus
that need not be total darkness). Based on this perceived response
of the circadian pacemaker, it was thought that intermittent
exposure to bright light could be nearly as effective as continuous
exposure to bright light.
While it is true that intermittent exposure to bright light can be
nearly as effective as continuous exposure to bright light, the
representation of the responsiveness of the circadian pacemaker as
shown in FIG. 2 was not accurate. On the contrary, it has been
recently discovered that the circadian pacemaker responds to light
stimuli in the manner shown in FIG. 3 and that only intermittent
pulses of light are required to effectively shift the circadian
phase.
The response curves of FIG. 3 are based on studies performed where
the subjects were exposed to 5 hour episodes of an intermittent
light stimulus with only 5 minutes of enhanced light per 25 minute
cycle. Each 25 minute cycle consisted of 1 minute of transition up
to enhanced light, a four minute pulse of enhanced light, 1 minute
of transition down to darkness, and a 19 minute pulse of darkness.
The phase shifts of those exposed to this intermittent light
stimulus were approximately half of those seen when giving subjects
5 hours of continuous lighting, even though the subjects were
exposed to light for only 20% of the episode of the light
stimulus.
Referring now to FIG. 3, it can be seen that during the first 5
minutes of the stimulus cycle the responsiveness of the circadian
pacemaker is initially high, but subsequently declines throughout
the duration of the 5 minute stimulus pulse. During the 19 minute
pulse of darkness, no response of the circadian pacemaker is
evoked. When the 5 minute light stimulus pulse is resumed, the
response of the circadian pacemaker is again initially high and
subsequently declines throughout the duration of the 5-minute
stimulus pulse. With the onset of the second 19 minute darkness
episode, the circadian pacemaker again becomes unresponsive.
The responsiveness of the circadian pacemaker to light (as shown in
FIG. 3) is based on the phenomenon of a "photic transducer" which
is comprised of a population of neuronal elements which are
responsive to light for a limited time period to "drive" or shift
the circadian pacemaker. These elements are not perpetually
responsive to light, as these elements are "burnedup" or "spent"
after an exposure period to light. This burning up of neuronal
elements is illustrated in FIG. 3 by downward sloping response ramp
A which elapses during the first 5 minutes of the stimulus episode.
After a certain period of time (which occurs during the darkness
episode) these elements are "recycled" at a predetermined rate, so
that they are once again responsive to light during the application
of the second 5 minute light stimulus pulse. The dynamic photic
transducer briefly described above with respect to FIG. 3 is
embodied in the improved method of the present invention and will
now be described in more detail below.
To accommodate the pseudo-saturation found in rodent responses, the
improved model of the present invention postulates a finite
population of potentially active neuronal elements that, in the
absence of light, I, are inactive, but are ready to be activated.
These are said to be in the "ready" state. Exposure to light
activates these neuronal elements. Activation of any particular
element is a probabilistic process and we let .alpha.(I) represent
the rate at which activation occurs for the population (i.e., the
fraction of the "ready" elements activated per minute). The
stronger I is, the larger .alpha. is. When activated, each element
rapidly initiates a chain of chemoelectric events which delivers a
"quantum" of drive to the circadian pacemaker, whereupon the
element is used-up and enters a subpopulation called "spent"
elements. A recycling process restores the "spent" elements to the
"ready" state at a rate .beta.(the fraction of "spent" elements
that are recycled per minute) which is independent of the light
intensity I.
This population of elements constitutes a dynamic photic transducer
which receives the light intensity pattern I(t) as an input and
delivers quantal flux, .delta.(t) as drive to the circadian
pacemaker. In the present model, the drive to the pacemaker depends
on the history of I(t), not simply its current value.
Letting n represent the fraction of all elements which are "spent"
at any given time, then (1-n) represents the fraction which are
"ready". The described rate processes lead to the differential
equation ##EQU1## Any protracted light level, I, will give a
constant value for .alpha.(I) and, in time, n will achieve a steady
level, n: ##EQU2## In particular, if I=0 we expect .alpha.(I)=0 and
n=0. That is, in the absence of photic stimulation all elements
revert to the "ready" state. For a steady I.noteq.0 there will be a
steady rate, .delta., at which quanta are delivered to the
pacemaker (the continuing rate at which recycled elements are
activated). The drive rate onto the pacemaker may be represented as
##EQU3## where the coefficient C is the product of the absolute
number of elements and the absolute drive strength of each quantum.
The right-hand-side of equation (3) has the standard form of the
logistic function (sometimes called the Naka-Rushton function or
the Michaelis function). However large the activation rate .alpha.
may be, .delta. can never exceed CB. In physical terms, when
.alpha.>>.beta. almost all the elements are in the "used"
state (n.congruent.1) and it is the recycle rate that limits the
rate at which elements can be continuously reactivated.
A most important feature of the photic transducer is its transient
response to the switching-on of light after extended darkness when
essentially all of the elements are in the "ready" state. Letting
time, t, be zero at the switch-on to light intensity, I, the
transient is given by
The right-side of equation (5) conveniently separates into two
terms. The first term is what would be expected from the
steady-state drive rate alone. We will call this the "sustained
response" rate, .delta..sub.sustained. The second term represents
the rapid activation of the reservoir of "ready" elements which
accumulated during the preceding darkness. We will call this the
"acute response" rate (to an acute stimulus), .delta..sub.acute. If
the light remains at I for some duration of time so that
(.alpha.(I)+.beta.)t>>1, the acute response will die out. The
cumulative drive due to the acute response is ##EQU4## The
cumulative acute response "saturates". If the stimulus is applied
for a duration, T, the cumulative sustained drive is simply
##EQU5## The cumulative sustained drive will equal the cumulative
acute drive for a time, T, which we denote by T.sub.critical :
The significance of this critical time value is that for stimulus
duration shorter than T.sub.critical the acute component dominates
the response while for durations longer than T.sub.critical the
sustained component dominates. With this model the
pseudo-saturation of rodent response corresponds to a dominance of
the acute component while the proportionality of response to
stimulus duration seen in humans corresponds to a dominance of the
sustained component. For strong stimuli, so that
.alpha.(I)>>.beta., n.congruent.1 and T.sub.critical is
dictated by .beta.. We conclude that .beta. for humans is
considerably larger than for rodents.
It is equally important to understand the prediction of this photic
transducer model in the case where a sustained light stimulus is
interrupted by an episode of darkness (I=0). Let the darkness begin
at t=0 and last for a duration, T. Before and after the darkness
the light has intensity I for which the corresponding n is given by
equation (2). Since I=0 implies .alpha.=0, no further activations
from the "ready" state occur once darkness is initiated.
Consequently the drive onto the pacemaker, .delta., is zero
throughout the dark episode 0.ltoreq.t.ltoreq.T. However, the
"spent" elements continue to be recycled during darkness, so n
decreases and the fraction of "ready" elements, 1-n, increases:
##EQU6## When the light is once again brought up to I at the end of
the dark episode there will be an acute drive component in addition
to the sustained drive. For t>T we have
for which the cumulative acute drive is ##EQU7## During the dark
episode there is a cumulative loss of sustained drive given by
C.beta.nT. This loss is partially offset by acute drive which
occurs when I is brought back.
The net loss is then ##EQU8## For .beta.T<<1 and a strong
stimulus (so n.congruent.1) the net loss of drive is very small.
This explains how there may be very little penalty for turning off
the stimulus completely for moderately long episodes provided light
is subsequently reinstated and the increased pool of "ready"
elements is utilized. Moreover, this model makes a specific
prediction of the manner in which the loss of drive depends on the
duration of the episode of darkness. The value of the recycle rate,
.beta., can be estimated from a single experiment as described in
detail below. The functional form can be validated by a series of
experiments with varying duration of darkness or diminished
light.
It should be understood that the intensity of light during a pulse
of enhanced light exposure may fall within a variety of ranges. For
example, the intensity of a pulse of enhanced light could fall
within a variety of ranges, including ranges of approximately
500-1,000 lux; 1,000-2,000 lux; 2,000-4,000 lux; and 4,000-100,000
lux. As stated previously, as the intensity increases the light
stimulus pulse would be able to activate more neuronal
elements.
The intensity of light during a pulse of reduced or diminished
light exposure may also fall within a variety of ranges. For
example, the intensity of a diminished light stimulus could fall
within the range of approximately 0-200 Lux; 0-10 lux; or 50-200
lux.
Nothing in the foregoing disclosure is intended to limit the
intensity range of an enhanced or diminished light stimulus to the
intensity ranges enumerated above. The key to determining whether a
particular intensity of light should be characterized as "enhanced"
or "diminished" with regard to a particular subject is the effect
of that light intensity on the circadian rhythm of the particular
subject to which it is applied, as well as the length of the
pulse.
Experiments to Evaluate Rate Parameters, .alpha.(I) and .beta.
Due to the "noise" in the assay of human circadian phase (random
fluctuations of temperature) experiments should be designed to
produce anticipated phase shifts of a few hours, at least.
Consequently bright light stimuli are commonly extended for 5
hours. Based on the evidence that response is approximately
proportional to stimulus duration when 3 hour and 5 hour durations
are compared, it is clear that in model terms both 3 hour and 5
hour >>T.sub.critical. The magnitude of T.sub.critical (and
consequently the size of .beta.) can best be estimated by embedding
darkness episodes of duration approximately equal to T.sub.critical
within the total stimulus window. The loss of cumulative drive
(evidenced as reduced phase shift compared to that achieved with no
darkness episodes) leads to an estimate of .beta. via equation
(12).
To enhance the phase shift reduction and thereby improve
experimental accuracy, several darkness episodes should be embedded
within the stimulus window, provided the duration of brightness
between the dark episodes is long enough to return the elements to
the steady-state level where the fraction of spent elements is n,
implying that the full cumulative acute drive given by equation
(11) is realized. This means that the duration of light between the
dark episodes should be long compared to the (.alpha.(I)).sup.-1.
Since we expect .alpha.>>.beta., this full realization of the
acute drive should be achieved if the intervening light episodes
are also approximately equal to T.sub.critical.
Once the estimate of .beta. is obtained from experiments in which
the stimulus consists of light and darkness episodes of
approximately equal duration, the value of .alpha.(I) can be
assessed by a pattern of interspersed light and dark episodes
within the stimulus window in which the duration of light episodes
is brief (somewhat less than (.alpha.(I)).sup.-1 so that acute
response is not fully realized. The dark episodes should have a
duration about half of T.sub.critical so that reduction of phase
shift, when it occurs, can be ascribed to incomplete acute
response.
As postulated, the activation rate, .alpha., depends on I and so
too does the sustained drive rate .delta. with a line (see equation
(8)). By comparing phase shifts produced by 5 hour stimuli of
different intensity (for which the acute component represents
little of the total drive) we are approximately comparing the
sustained drive rates at the different intensities. Equation (3)
enables us to infer the corresponding .alpha.(I). In a wide variety
of studies of phototransduction where data are fit by a logistic
function such as equation (3) it has proven useful to let
wherein I.sub.o establishes the reference intensity for which
.alpha.=1 (in whatever units of time have been chosen; minutes
here) while the exponent p is typically less than 1 and usually in
the range 0.6.ltoreq.p .ltoreq.0.9. For humans, we estimate p=0.85
and I.sub.o =30,000 lux. (These parameters are estimated by fitting
phase shift data at various light intensities with the logistic
equation (2). The value of .beta. is found from experiments in
which light and dark episodes alternate within the stimulus
window.) With I=30,000 lux, the activation rate, .alpha., will be 1
min.sup.-1. For comparison, the hamster data from Nelson et al. are
best fitted by p=0.6 and I.sub.o =10 lux, the latter corresponding
to the enhanced visual sensitivity of rodents vis-a-vis humans.
In neuronal processes, response to a stimulus often is found only
after some threshold stimulus is attained. We anticipate that at
very low levels of I the transition rate .alpha.(I) may be zero, so
that only after I is raised to some critical level will any
response be observed. Since, in a population of potentially active
neuronal elements the individual elements would very likely have
different threshold levels, distributed statistically, the
transition between .alpha.(I)=(I/I.sub.o).sup.p and .alpha.(I)=0
will not be abrupt. There is evidence that hamster response has a
threshold at about 0.1 lux. Human response shows no threshold
behavior for I as low as 150 lux.
We have performed experiments in which a single 5 hour stimulus is
subdivided into 4 bright light (10,000 lux) episodes with three
interspersed dark (less than 1 lux) episodes all of approximately
equal duration (.congruent.42 minutes). From these we have inferred
that the recycle rate, .beta., is approximately 0.02 min.sup.-1. No
other comparable experiments for hamsters are known, but by
comparing phase shifts obtained (by various investigators) with
sustained light durations of 5, 10, 15, and 60 minutes, we infer
that .beta. is approximately 0.01 min.sup.-1 or about 50% of the
human recycle rate.
Photic Transducer Model Summary
The essential equation is (1) ##EQU9## The activation rate constant
.alpha. is a function of I for which we have selected the form
where I.sub.o and p are constants. For any specified temporal
pattern of light, I(t), equation (13) gives .alpha.(t). Integration
of equation (1) gives n(t). The drive onto the pacemaker is then
given by
In general the integration of (1) must be done numerically.
Selected analytic integrals for I(t) that change stepwise have been
developed above.
The present best estimates for model parameters are
.beta.=0.02 min.sup.-1
I.sub.o =30,000 lux (with .alpha. measures in min.sup.-1)
p=0.85
The coefficient C is evaluated by making the steady drive, .delta.,
for 10,000 lux match the value B=CI.sup.1/3 =0.018 (10,000).sup.1/3
=0.388, of the direct-drive model:
.alpha.(10,000)=(1/3).sup.0.85 =0.393 min.sup.-1
n(10,000)=0.393/(0.393+0.02)=0.952
C=0.388/(1-0.952)(0.393)=11.0
Further Signal Processing
The photic transducer model described above very simply encompasses
two of the most important nonlinear aspects of the response of the
circadian pacemaker to photic stimulation. One is the temporal
pseudo-saturation seen in those animals for which the pacemaker
drive is dominated by the acute component. The other is the
intensity saturation effect found in the sustained component (see
equation (2)) and evidenced in human response that is typically
dominated by sustained drive effects.
It is useful to examine the consequences of interposing a linear
temporal filter between the photic transducer output, .delta.(t),
and the pacemaker. One of the simplest filters is described by a
first-order differential equation, ##EQU10## where B is the filter
output (and hence represents the drive onto the pacemaker). T.sub.f
is the filter time constant. This filter has the properties of
smoothing the .delta.(t) and, in an approximate sense, delaying the
smoothed version by T.sub.f. The long-time integral of B is equal
to that of .delta., so the integrated strength of the drive to the
pacemaker is unchanged by the filter. In the case of a hamster
exposed to a 5 minute pulse of 20 lux of brightness, the acute
response of .delta.(t) will be essentially complete at the end of
the pulse. Moreover, the turning-off of the light at the end of the
pulse means that no further drive can be generated. The
interposition of a filter of the type described implies that the
filter output drive to the pacemaker, B, may be considerably
extended, declining exponentially with a time constant T.sub.f.
A very interesting situation arises if T.sub.f is matched to the
recycle rate constant .delta.:
Equation (1) can be simply rearranged ##EQU11## so that the right
side is exactly .delta.(t). The left side can be rewritten
##EQU12## comparison of equation (15) with equation (14) shows that
in this special case
That is, the output of the matched filter is equal to n (the
fraction of "spent"e elements) multiplied by the recycle rate
constant, .beta..
The combination of the photic transducer with following matched
filter leads to a second model interpretation. In this
interpretation, we suppose that transducer elements, upon
activation, enter a state of sustained drive onto the pacemaker
(rather than delivering only a quantum of drive). In such a case,
the drive to the pacemaker at any time will be proportional to n
(the fraction of elements which have been activated). The recycle
rate, .beta., now represents the rate at which active elements
cease being active. In this view, when an episode of light is
initiated from a state of protracted darkness, the drive to the
pacemaker will progressively increase as elements are activated
(moved to the state represented by the fraction n) up to the level
n. When the light is then turned off, drive to the pacemaker will
continue while the fraction n declines exponentially with the time
constant .beta..sup.-1. This model may be called an "element
recruitment" model wherein the "ready" elements are recruited into
extended activation. Equations (15) and (16) show that the
"expenditure" model with the matched filter added is the
mathematical equivalent of the "recruitment" view.
The question of whether a filter such as (14) exists in the signal
pathway is difficult to appraise experimentally and is largely
moot. First, the response processes within the pacemaker itself are
integrative, and so change very little with input signal smoothing.
Secondly, any delay produced by the filter can simply be
accommodated as a change in the presumed timing of the phase
response curve (PRC) relative to other circadian markers. Only when
the physiology of the internal pacemaker mechanism is elucidated
can this question be properly addressed
It is important to observe that light input mediating other
biological effects such as melatonin suppression or alertness
enhancement may operate via the same photic transduction mechanism
as that which mediates effects on the circadian pacemaker.
Significance of Representation of Photic Transducer Function
Heretofore, the conventional view of the action of light on the
circadian pacemaker implied that a brief reduction of stimulus
(such as might be produced by directing one's gaze away from a
bright light source) would invoke a penalty in the cumulative
stimulus effect. Through a series of experiments employing unique
temporal patterns of bright and dark episodes contained within the
overall stimulus time-window we have demonstrated that even long
(e.g., 30 minute) intervals in which light is completely absent can
be accommodated with relatively little penalty, provided these are
followed by sufficiently long (e.g., 5-10 minute) episodes of
bright light. This discovery greatly enhances the applicability of
bright light interventions in the workplace, in phototherapy
routines and for personal use (for example, in preventing jet lag).
For example, in industrial situations where the job may call for
some duties in a dark or dimly lit environment, the use of bright
light to produce adaptation to shift rotation need not be
compromised.
Since the required duration of bright episodes is related to the
activation rate, .alpha., which is itself strongly dependent on
light intensity, I, the prescription for temporal light patterning
changes with the brightness of available light. The mathematical
representation of the photic transducer permits an optimal
accommodation to any imposed limitations of brightness or work
schedule.
Based on prior modelling work, it is known that for extended
durations of light exposure (e.g., 3 to 5 hours) the penalties to
be paid by lowering light intensity from about 10,000 lux to 3,000
lux were modest. The relationship B=CI.sup.1/3 predicts only a 33%
decrease in drive to the pacemaker for this more than threefold
reduction of light intensity. Recent data at 1250 lux imply the
decrease in pacemaker drive is even smaller than this prediction.
Seemingly, there is little profit in pursuing very large I.
However, transducer models shows that when intermittent bright
light patterning is considered, 10,000 lux actually has a very
special advantage over 3,000 lux, by allowing a much lower fraction
of rime during which the light need Be applied to provide a desired
effect (known as a shorter "duty cycle"). One simple consequence
that can be deduced from the model is that if all light and dark
episodes are Brief (i.e., less than about 1 minute) the her effect
is equivalent to a steady intensity whose .alpha.value is that of
the actual reduced By the fraction of time that the light episodes
represent.
For example, if 10,000 lux is viewed for 50% of the rime (and
darkness for the other 50% ), the equivalent steady intensity is
that for which .alpha.1/2 times .alpha.(10,000). Using the exponent
p=0.85 gives an equivalent steady intensity of 4,400 lux. Put
another way, the availability of 10,000 lux allows a duty cycle of
0.5 (for rapid intermittence) with the equivalent of 4400 lux. With
our current estimate of photic transducer parameters, equations (2)
and (3) predict that the loss in drive to the pacemaker will Be
less than 5%. A similar calculation for a duty cycle of 0.2 (20% of
at 10,000 lux and 80% of the time at 0 lux) gives an equivalent
steady I of 1,505 lux and a reduction of pacemaker drive of
16%.
Devices Capable of Utilizing the Photic Transducer Model of the
Present Invention
The use of intermittent light schedules offers a special
opportunity for devices by means of which a person can monitor the
status of his/her photic transducer. In particular, by monitoring
light exposure with a tiny ambulatory lux meter and feeding such
data to a special purpose microcomputer that integrates equation
(1), the user can obtain on-line an output portraying both the
correct level of "ready" and "spent" elements and also the
cumulative drive delivered to the circadian pacemaker from any
chosen start time. If the user has remained away from suitably
bright light for too long a time, a warning reminder can be
sounded. In this way, the user can achieve desired objectives for
manipulating the circadian pacemaker (both Type 1 and Type 0)
resetting) without personal attention to minute-by-minute light
exposure. Moreover, it is seldom that intermittent light patterns
will be a simple mixture of bright episodes and totally dark
episodes. Rather, a continuous pattern of variations from quite
bright to quite dim light will be more common, and online
computation is almost essential to avoid serious stimulus lapses
which could strongly reduce cumulative drive. This is especially
important where light in evening hours is called for, since normal
environmental light is not strong and serious effort is required to
access bright light.
At a higher level, the measured pacemaker drive can be applied to a
computer replica of the pacemaker itself and the overall phase and
amplitude status of the pacemaker displayed. Those capabilities are
especially important if the user is planning to achieve maximum
phase shifting effects by type 0 resetting (i.e., suppression of
circadian amplitude en route to the final desired state). It should
be remembered that efficient resetting of the circadian pacemaker
requires avoidance of light drive at certain times as well as
strong delivery of light at other times. If a computer replica of
the pacemaker is available and the resetting objectives are read
in, an output indicating when light is to be avoided can be easily
generated. When combined with the aforementioned photosensor,
warning signals can be produced. This can be important since the
photic transducer model implies that relatively brief (e.g. a few
minutes) exposure to unwanted light can produce significant adverse
drive to the pacemaker.
The computation that monitors the ready/spent status of the photic
transducer operates on a time scale of minutes to a few hours. The
computation that estimates the status of the circadian pacemaker
itself is necessarily operating on the circadian time scale.
The improved method described herein may be applied to other
settings or devices to efficiently effect modification of the
circadian phase. For example, a lounge used by shift workers could
be equipped with bright lights and a timing device which has been
programmed in accordance with the improved model of the present
invention.
Another example of an application of an intermittent light stimulus
would involve a pair of eyeglasses with means for exposing the
wearer to light of selected intensity at selected times. Such
eyeglasses could be used, for example, by those travelling across
time zones or by shift workers. Because the light source would be
close to the eyes of the wearer, and because the light stimulus
would be intermittent, very little power would be required for such
a device. A similar light emitting device could be similarly
incorporated into a visor or hat.
Yet another example of an application of the method of the present
invention would be to mount a light source and a control mechanism
onto the headboard of a bed, or other lounging location where the
user is likely to be when the light stimulus is to be applied. It
is envisioned that such a device could be small enough to be
carried by a traveler, for example.
The method of the present invention may be further applied to any
of the devices disclosed in the parent patents described at the
beginning of this application, the disclosures of which being
incorporated in their entirety herein by reference.
Theoretical Foundations for Modifying the Circadian Phase and
Amplitude
The endogenous (deep) circadian pacemaker, hereafter designated as
"the x oscillator," or simply "x," may be modelled mathematically
by a second-order differential equation of the van der Pol type,
specifically: ##EQU13##
In the absence of any forcing function, F.sub.x, x will have an
approximately sinusoidal waveform with an amplitude of 1 (that is,
the full excursion of x from a maximum of +1 to a minimum of -1
will be 2).
The forcing function, F.sub.x, consists of two effects. The
dominant effect is that of the light to which the retina is
exposed. The secondary effect is due to endogenous internal
influences of the activity-rest pattern.
In the form given above, time t is measured in clock hours. The
parameter m.sub.x is the "stiffness" of the x oscillator and for
normal humans is expected to be in the range 0.05 .ltoreq.m.sub.x
.ltoreq.0.15 with 0.1 as the representative value. The estimate of
0.1 for m.sub.x was originally chosen as a trial value by analogy
with the value of m.sub.y (the internal "stiffness" of the y
oscillator) of our dual oscillator model of the human circadian
timing system which had been validated by earlier experimentation
characterizing a phenomenon called phase trapping. Our experimental
success in manipulating the amplitude of the oscillatory output
implies that m.sub.x is very unlikely to be larger than 0.15, and
certainly not larger than 0.2. An oscillator with an internal
stiffness coefficient less than 0.03 would be unreasonably
susceptible to external influences and therefore physiologically
incompatible with the observed robustness of the endogenous
circadian ("x") oscillator sensitive in this context. The parameter
.tau..sub.x represents the intrinsic period of the x oscillator and
for normal humans is expected to be in the range
23.6<.tau..sub.x .ltoreq.25.6 with 24.6 as the representative
value.
For most people in the age range 5 to 55 years, sleep occurs in a
single consolidated episode each 24 hour day. In the laboratory
paradigm of "free run" (self-selected sleep and wake) the
sleep/wake cycle time for young adults is typically in the 25 to 26
h range. About 30% of free run experiments lead spontaneously to
internal desynchrony in which the sleep/wake cycle time exceeds 30
hours (ranging up to 50 hrs) while the core body temperature rhythm
proceeds at about 24.5 h. We ascribe these separate rhythms to
distinct rhythm generators: y for the labile sleep/wake process and
x for the "deep circadian pacemaker". In synchronized free run the
interactions between y and x produce mutual entrainment, and since
the compromise cycle time, .tau., is biased strongly toward
.tau..sub.x, it follows that the action of y on x is only about 25%
of the action of x on y.
Enhanced Model
In its simplest form, the model is ##EQU14## in which the drive of
light on the circadian system is only in the X equation. The
sensitivity function, B, includes the cube-root relationship for
physical light intensity and the term -mx is included to provide a
circadian modulation of the sensitivity based on the known
modulation of visual sensitivity (hence m=1/3 was chosen).
In a recent modification, the light was also permitted to act on
the X.sub.c equation ##EQU15## where q=1 was indicated at that
time. It now appears that a reduced value q=0.3 or 0.4 is
preferred.
A much more thorough appraisal of data has indicated two additions
to the sensitivity function:
with k=1/3 and h=1/2 as preferred values. The term k X.sub.c (when
combined with the original m X term) serves to advance the
circadian phase at which maximum sensitivity of the circadian
system to light occurs, by approximately three hours. It also
increases the amount of sensitivity modulation which occurs over
the circadian cycle. The term hX.sub.c.sup.2 acts to reduce
sensitivity to light at circadian phases which are about .+-.6
hours from the nadir of the circadian cycle (which nadir is
typically about 5 AM for normally entrained persons). Overall, this
circadian sensitivity function is considerably different from human
visual sensitivity measured throughout the day and night and
reflects a current appraisal of the acute action of light on the
circadian pacemaker, when it has a rhythm amplitude close to
nominal (an amplitude of 1 in the mathematical model).
Finally, the action of light in the X.sub.c equation is altered by
two additional terms, (a-bx) ##EQU16## where a=0.1 and b=0.1. These
terms are included so that, with the corrections in the B-function
just described, the phase shift observed when light is applied near
the phase of the nadir of X is properly reproduced. Put another
way, the original simple model did a good job when light was
applied at the nadir of X but had other deficiencies. When the
B-function was modified to address these deficiencies, we end up
with errors for light applied at the nadir and the a-bX terms
correct these.
Thus, the enhanced model is expressed by ##EQU17## where:
.tau..sub.x =24.2 .mu.=0.13 c=0.18
m=1/3 k=1/3 h=0.5
a=0.1 b=0.1 q=0.3
While the method of the present invention has been disclosed in
connection with the preferred embodiment thereof, it should be
understood that there are alternative realizations of the model
which fall within the spirit and scope of the invention as defined
by the following claims.
* * * * *